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This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we…

Information Theory · Computer Science 2025-07-14 Akram Baghban , Marc Newman , Anna-Lena Horlemann , Mehdi Ghiyasvand

An $(n,r,h,a,q)$-Local Reconstruction Code (LRC) is a linear code over $\mathbb{F}_q$ of length $n$, whose codeword symbols are partitioned into $n/r$ local groups each of size $r$. Each local group satisfies `$a$' local parity checks to…

Information Theory · Computer Science 2022-05-20 Sivakanth Gopi , Venkatesan Guruswami

Repair locality is a desirable property for erasure codes in distributed storage systems. Recently, different structures of local repair groups have been proposed in the definitions of repair locality. In this paper, the concept of…

Information Theory · Computer Science 2014-10-20 Anyu Wang , Zhifang Zhang

In this paper, we propose several constructions of Locally Recoverable Codes from elliptic surfaces. In particular, we are able to obtain codes with availability $t>2$, codes with hierarchical locality and, finally, codes which combine…

Information Theory · Computer Science 2026-05-28 Elena Berardini , Andrea Fornetto

Locally repairable codes (LRCs) have received significant recent attention as a method of designing data storage systems robust to server failure. Optimal LRCs offer the ideal trade-off between minimum distance and locality, a measure of…

Information Theory · Computer Science 2024-02-07 Allison Beemer , Ryan Coatney , Venkatesan Guruswami , Hiram H. López , Fernando Piñero

A code over a finite alphabet is called locally recoverable (LRC code) if every symbol in the encoding is a function of a small number (at most $r$) other symbols of the codeword. In this paper we introduce a construction of LRC codes on…

Information Theory · Computer Science 2016-11-17 Alexander Barg , Itzhak Tamo , Serge Vladuts

Constructions of optimal locally repairable codes (LRCs) achieving Singleton-type bound have been exhaustively investigated in recent years. In this paper, we consider new bounds and constructions of Singleton-optimal LRCs with minmum…

Information Theory · Computer Science 2022-07-13 Weijun Fang , Bin Chen , Shu-Tao Xia , Fang-Wei Fu

We introduce a family of balanced locally repairable codes (BLRCs) $[n, k, d]$ for arbitrary values of $n$, $k$ and $d$. Similar to other locally repairable codes (LRCs), the presented codes are suitable for applications that require a low…

Information Theory · Computer Science 2020-02-14 Katina Kralevska , Danilo Gligoroski , Harald Øverby

Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. This paper investigates a generalization of the usual locally…

Information Theory · Computer Science 2016-01-28 Ankit Singh Rawat , Arya Mazumdar , Sriram Vishwanath

Locally recoverable codes (LRCs) were proposed for the recovery of data in distributed and cloud storage systems about nine years ago. A lot of progress on the study of LRCs has been made by now. However, there is a lack of general theory…

Information Theory · Computer Science 2021-02-02 Pan Tan , Cuiling Fan , Cunsheng Ding , Zhengchun Zhou

In this paper, the repair problem for erasures beyond locality in locally repairable codes is explored under a practical system setting, where a rack-aware storage system consists of racks, each containing a few parity checks. This is…

Information Theory · Computer Science 2024-07-29 Han Cai , Ying Miao , Moshe Schwartz , Xiaohu Tang

We present the construction of a new family of erasure correcting codes for distributed storage that yield low repair bandwidth and low repair complexity. The construction is based on two classes of parity symbols. The primary goal of the…

Information Theory · Computer Science 2015-08-28 Siddhartha Kumar , Alexandre Graell i Amat , Iryna Andriyanova , Fredrik Brännström

Typically, locally repairable codes (LRCs) and regenerating codes have been studied independently of each other, and it has not been clear how the parameters of one relate to those of the other. In this paper, a novel connection between…

Information Theory · Computer Science 2016-11-22 Toni Ernvall , Thomas Westerbäck , Ragnar Freij-Hollanti , Camilla Hollanti

In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position $P$ of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $R_P$. The codes in the class…

Information Theory · Computer Science 2021-07-29 Cícero Carvalho , Victor G. L. Neumann

We first give a construction of binary $t_1$-deletion-$t_2$-insertion-burst correcting codes with redundancy at most $\log(n)+(t_1-t_2-1)\log\log(n)+O(1)$, where $t_1\ge 2t_2$. Then we give an improved construction of binary codes capable…

Information Theory · Computer Science 2022-11-23 Zuo Ye , Ohad Elishco

We consider the problem of constructing binary codes for correcting deletions that are localized within certain parts of the codeword that are unknown a priori. The model that we study is when $\delta \leq w$ deletions are localized in a…

Information Theory · Computer Science 2021-01-11 Serge Kas Hanna , Salim El Rouayheb

Cooperative regenerating codes are regenerating codes designed to tradeoff storage for repair bandwidth in case of multiple node failures. Minimum storage cooperative regenerating (MSCR) codes are a class of cooperative regenerating codes…

Information Theory · Computer Science 2019-01-29 Bh. Rekha Devi , V. Lalitha

Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, $ \partial - 1 $ erasures per local group), and…

Information Theory · Computer Science 2020-12-08 Umberto Martínez-Peñas , Diego Napp

In an $[n,k,d]$ linear code, a code symbol is said to have locality $r$ if it can be repaired by accessing at most $r$ other code symbols. For an $(n,k,r)$ \emph{locally repairable code} (LRC), the minimum distance satisfies the well-known…

Information Theory · Computer Science 2017-02-21 Jie Hao , Shu-Tao Xia , Bin Chen

Locally repairable codes(LRCs) play important roles in distributed storage systems(DSS). LRCs with small locality have their own advantages since fewer available symbols are needed in the recovery of erased symbols. In this paper, we prove…

Information Theory · Computer Science 2022-07-08 Yuan Gao , Siman Yang